Perpetuity Calculator

Perpetuity Type:

Zero-Growth Growing

Payment ($):

Discount Rate (%):

Growth Rate (%):

1. What is the Perpetuity Calculator?

Definition: The Perpetuity Calculator computes the present value of an infinite series of equal cash flows received at regular intervals, with options for zero-growth or growing perpetuities.

Purpose: It helps investors and financial analysts value financial instruments like preferred stocks or consols, which provide perpetual payments, aiding in investment decisions.

2. How Does the Calculator Work?

The calculator uses the following formulas:

$ \text{PV} = \frac{\text{P}}{\text{R}} $ (Zero-Growth)

$ \text{PV} = \frac{\text{P}}{(\text{R} - \text{G})} $ (Growing)

Where:

$ \text{PV} $: Present Value ($);
$ \text{P} $: Payment ($), the cash flow per period;
$ \text{R} $: Discount Rate (decimal);
$ \text{G} $: Growth Rate (decimal, for growing perpetuity).

Steps:

Select the perpetuity type: Zero-Growth or Growing.
Enter the payment amount per period.
Enter the discount rate as a percentage.
For Growing Perpetuity, enter the growth rate as a percentage (must be less than the discount rate).
Calculate the present value using the selected formula.
Display the result in dollars, formatted in scientific notation if the absolute value is less than 0.001, otherwise with 4 decimal places.

3. Importance of Perpetuity Calculation

Calculating perpetuity is essential for:

Valuation of Assets: Determines the present value of perpetual cash flows like dividends or rents.
Investment Analysis: Supports valuation of financial instruments with infinite horizons.
Financial Planning: Aids in assessing long-term financial commitments or returns.

4. Using the Calculator

Example 1 (Zero-Growth): Calculate the present value of a perpetuity with a $1,000 annual payment and a 5% discount rate:

$ \text{P} $: $1,000;
$ \text{R} $: 5%;
$ \text{PV} $: $ \frac{1000}{0.05} = 20,000 $.

Example 2 (Growing): Calculate the present value with a $1,000 initial payment, 5% discount rate, and 2% growth rate:

$ \text{P} $: $1,000;
$ \text{R} $: 5%;
$ \text{G} $: 2%;
$ \text{PV} $: $ \frac{1000}{0.05 - 0.02} = 33,333.33 $.

5. Frequently Asked Questions (FAQ)

Q: What is a perpetuity?
A: A perpetuity is a stream of equal cash flows that continues indefinitely, such as certain bonds or preferred stocks.

Q: Why must the growth rate be less than the discount rate?
A: If the growth rate equals or exceeds the discount rate, the present value becomes infinite, which is not feasible.

Q: Can perpetuities exist in practice?
A: Yes, examples include consols (redeemed in 2015) and some preferred stocks, though they are rare today.